[Cujster]

I've experienced precisely the same problem that you've indicated with my 2000 Blazer LT with the 4 mode (2H, 4H, 4L, Auto4) electronic shift case.

After verifying that the actuator, 4WD front axle solenoid (the one mounted on the firewall) and that the diaphram was good, I swapped out the transfer case control module with a co-workers 2001 LT and found that solved the problem: bad module. To be more precise, there are two double-pole relays on that module and one went bad.
In any case, I purchased and installed a new one and am now shifting on-the-fly with ease!

In order to get the transfer case shift actuator to kick the transfer case back into 2Hi, you can disconnect the front axle 4WD sensor, then start up your Blazer and drive normally. Within 60 seconds the module will determine that it cannot tell whether the front axle is engaged so it will default the transfer case back into 2 WD. That is IF your actuator is functioning properly. However, as you mentioned that your dealer indicated the module needs replacement, so this should work for you.
Once in 2WD mode, reconnecting the 4WD sensor on the front axle will not cause it to switch back into 4WD unless you press either the Auto4WD or 4Hi button.

(It will not go into 4Lo without both the tranfer case and gear in neutral)

The 4WD front axle sensor is located on the front side of the front axle near the centerline of the Blazer, slightly closer to the passenger side.
The connector is a simple two-wire connector that can be snapped off with your fingers.

According to the Helms manuals (which I have) for the Blazer, the transfer case control module runs a diagnostic on itself when you turn on the ignition key.
It checks the RAM and ROM then each relay. It has positive feedback determining whether each relay is in the commanded position. If one of the relays fail (which happened in my case) and it doesn't pass it's own diagnostic test, it then freezes all transfer case shifting for the duration of that ignition cycle (until you turn the key off) and you'll only see the 4WD switch lights flash.

I don't want to stretch this reply out too long, but feel free to E-mail me if you'd like to understand what components perform what functions within the NVG-236/246 NP-8 electronic transfer case system that you have.

The transfer case control module is located behind the plastic panel just to the right of a passengers feet. This panel is held in place by several "snaps" and requires no tools to remove it.
Once you get to the module, you'll need a 10mm socket wrench to remove the 3 mounting nuts. There are two harnesses connected into it which can be snapped loose with a small flat blade screwdriver.

I priced this module at the local dealer and they quoted me a price of $408. I purchased mine at gmpartsdirect.com for $278 (including shipping & handling). It took less than 10 minutes to replace it.

To verify that your control module is the same as I expect, it will have the part number on it of: 15748800
This is the OEM part number but has since been replaced with 12577412.

Hope this information helps.

Regards,
Cujster